The problem of -simple spectrum for ergodic group automorphisms
The quasi-sure ratio ergodic theorem
The rate of convergence of iterates of the Frobenius-Perron operator for piecewise monotonic transformations
The rearrangement inequality for the ergodic maximal function.
The return time theorem fails on infinite measure-preserving systems
The rotation number of some transformation related to billiards in an ellipse
The sequence entropy for Morse shifts and some counterexamples
The spectrum and commutant of a certain weighted translation operator.
The Speed of Convergence in Ergodic Theorem.
The Stein-Weiss theorem for the ergodic Hilbert transform
The Stein-Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of E depends only on the measure of E is generalized for the ergodic Hilbert transform in the case of a one-parameter flow of measure-preserving transformations on a σ-finite measure space.
The topological centralizers of Toeplitz flows and their Z2-extensions.
The topological centralizers of Toeplitz flows satisfying a condition (Sh) and their Z2-extensions are described. Such Toeplitz flows are topologically coalescent. If {q0, q1, ...} is a set of all except at least one prime numbers and I0, I1, ... are positive integers then the direct sum ⊕i=0∞ Zqi|i ⊕ Z can be the topological centralizer of a Toeplitz flow.
The variational principle
The vector individual weighted ergodic theorem for bounded Besicovich sequences.
The σ-ideal of closed smooth sets does not have the covering property
We prove that the σ-ideal I(E) (of closed smooth sets with respect to a non-smooth Borel equivalence relation E) does not have the covering property. In fact, the same holds for any σ-ideal containing the closed transversals with respect to an equivalence relation generated by a countable group of homeomorphisms. As a consequence we show that I(E) does not have a Borel basis.
Théorème ergodique ponctuel pour les suites uniformes
Théorème ergodique ponctuel pour un semi-groupe commutatif finiment engendré de contractions de
Théorème ergodique presque sous-additif et convergence en moyenne de l'information
Théorèmes ergodiques multidimensionnels et suites aléatoires universellement représentatives en moyenne
Théorèmes ergodiques ponctuels pour des mesures diagonales. Cas des systèmes distaux
Théorèmes ergodiques pour des mesures diagonales